How many four-digit numbers can be formed by using the digits 1, 2, 3, 4, 5, 6, 7 if at least one digit is repeated.

Explanation

The numbers that can be formed when repetition of digits is allowed are `7^(4)=2401`.
the number that can be formed when all the digits are distincct when repetition is not allowed are `.^(7)P_(4)=840`.
therefore, the numbers that can be formed when atleast one digit is repeated `=7^(4)-.^(7)P_(4)`
`=2401-840=1561`